Question

The mean of marks scored by $100$ students was found to be $40.$ Later on it was discovered that a score of $53$ was misread as $83.$ Find the correct mean.

Answer 1

Mean score of students $=40$

∴Total score $=100\times 40=4000$ 100

[$\because$ Mean $=\frac{\text{Sum of the score of all students (Total score)}}{\text{Number of students}}$]

Difference in one score by mistake $=83-53=30$

Actual total scores $=4000-30=3970$

Actual mean $=\frac{\text{Actual total scores}}{\text{Number of students}}=\frac{3970}{100}=39.70$